In this lesson, we learn about limit cycles, which are closed trajectories in a nonlinear autonomous system that represent periodic behavior. Limit cycles are isolated and stable, meaning nearby points approach the cycle, and they are of interest in modeling natural phenomena that exhibit periodic motion. The existence of limit cycles is difficult to determine, but two theorems are presented for non-existence criteria: Bendixson's criterion and a criterion involving critical points. Bendixson's criterion involves calculating the divergence of the vector field and can be proven using 1802-level math.
Limit Cycles: Existence and Non-existence Criteria -- Lecture 32. Learn about limit cycles and their criteria.
Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 29, 2008). License: Creative Commons BY-NC-SA.
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